KasturiRanganR4/5.2_notebook_quizz_numpy2d.ipynb

## 5.2_notebook_quizz_numpy2d.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Get to Know a numpy Array </h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will use the numpy array <code> A</code> for the following "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "A=np.array([[11,12],[21,22],[31,32]])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) type using the function type "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2) the shape of the array "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3) the type of data in the array "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4) Find the second row of the numpy array <code>A</code>:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([21, 22])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Two kinds of Multiplying  </h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "you will use the following numpy arrays for the next questions "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "A=np.array([[11,12],[21,22]])\n",
    "B=np.array([[1, 0],[0,1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) multiply array <code> A </code> and <code>B</code>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11,  0],\n",
       "       [ 0, 22]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A*B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2)  plot the function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[11 12]\n",
      " [21 22]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f602005d080>,\n",
       " <matplotlib.lines.Line2D at 0x7f602005d1d0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "C=np.dot(A,B)\n",
    "D=np.dot(B,A)\n",
    "print(C)\n",
    "plt.plot(C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "<small>Copyright &copy; 2018 IBM Cognitive Class. This notebook and its source code are released under the terms of the [MIT License](https://cognitiveclass.ai/mit-license/).</small>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python",
   "language": "python",
   "name": "conda-env-python-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"<h3> Get to Know a numpy Array </h3>"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"You will use the numpy array <code> A</code> for the following "
	]
	},
	{
	"cell_type": "code",
	"execution_count": 1,
	"metadata": {},
	"outputs": [],
	"source": [
	"import numpy as np\n",
	"A=np.array([[11,12],[21,22],[31,32]])\n"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"1) type using the function type "
	]
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"numpy.ndarray"
	]
	},
	"execution_count": 2,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"type(A)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"2) the shape of the array "
	]
	},
	{
	"cell_type": "code",
	"execution_count": 3,
	"metadata": {
	"collapsed": false,
	"jupyter": {
	"outputs_hidden": false
	}
	},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"(3, 2)"
	]
	},
	"execution_count": 3,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"A.shape"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"3) the type of data in the array "
	]
	},
	{
	"cell_type": "code",
	"execution_count": 4,
	"metadata": {
	"collapsed": false,
	"jupyter": {
	"outputs_hidden": false
	}
	},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"dtype('int64')"
	]
	},
	"execution_count": 4,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"A.dtype"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"4) Find the second row of the numpy array <code>A</code>:"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 5,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"array([21, 22])"
	]
	},
	"execution_count": 5,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"A[1]"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"<h3> Two kinds of Multiplying </h3>"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"you will use the following numpy arrays for the next questions "
	]
	},
	{
	"cell_type": "code",
	"execution_count": 6,
	"metadata": {},
	"outputs": [],
	"source": [
	"A=np.array([[11,12],[21,22]])\n",
	"B=np.array([[1, 0],[0,1]])"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"1) multiply array <code> A </code> and <code>B</code>"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 7,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"array([[11, 0],\n",
	" [ 0, 22]])"
	]
	},
	"execution_count": 7,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"A*B"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"2) plot the function"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 13,
	"metadata": {},
	"outputs": [
	{
	"name": "stdout",
	"output_type": "stream",
	"text": [
	"[[11 12]\n",
	" [21 22]]\n"
	]
	},
	{
	"data": {
	"text/plain": [
	"[<matplotlib.lines.Line2D at 0x7f602005d080>,\n",
	" <matplotlib.lines.Line2D at 0x7f602005d1d0>]"
	]
	},
	"execution_count": 13,
	"metadata": {},
	"output_type": "execute_result"
	},
	{
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"needs_background": "light"
	},
	"output_type": "display_data"
	}
	],
	"source": [
	"import matplotlib.pyplot as plt\n",
	"C=np.dot(A,B)\n",
	"D=np.dot(B,A)\n",
	"print(C)\n",
	"plt.plot(C)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"<hr>\n",
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